Two-Bit Bit Flipping Decoding of LDPC Codes

In this paper, we propose a new class of bit flipping algorithms for low-density parity-check (LDPC) codes over the binary symmetric channel (BSC). Compared to the regular (parallel or serial) bit flipping algorithms, the proposed algorithms employ one additional bit at a variable node to represent its "strength." The introduction of this additional bit increases the guaranteed error correction capability by a factor of at least 2. An additional bit can also be employed at a check node to capture information which is beneficial to decoding. A framework for failure analysis of the proposed algorithms is described. These algorithms outperform the Gallager A/B algorithm and the min-sum algorithm at much lower complexity. Concatenation of two-bit bit flipping algorithms show a potential to approach the performance of belief propagation (BP) decoding in the error floor region, also at lower complexity.Comment: 6 pages. Submitted to IEEE International Symposium on Information Theory 201

Error Correction Capability of Column-Weight-Three LDPC Codes Under the Gallager A Algorithm—Part II

The relation between the girth and the error correction capability of column-weight-three LDPC codes under the Gallager A algorithm is investigated. It is shown that a column-weight-three LDPC code with Tanner graph of girth g ¿ 10 can correct all error patterns with up to (g /2-1) errors in at most g /2 iterations of the Gallager A algorithm. For codes with Tanner graphs of girth g ¿ 8, it is shown that girth alone cannot guarantee correction of all error patterns with up to (g /2-1) errors under the Gallager A algorithm. Sufficient conditions to correct (g /2-1) errors are then established by studying trapping sets.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]